On 2/14/04 at 10:19 PM, nma124 at hotmail.com (steve_H) wrote:
>Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message
>news:<c0kr0g$fo8$1 at smc.vnet.net>...
>>Quite apart from that, the order of evaluation is a key issue in
>>functional programming languages and there are lots of cases where
>>Mathematica will produce different answers if you change the order
>>of evaluation even if "mathematically" you are computing the same
>>thing.
>Ok, that is my main point then. All what I was saying is that we
>are looking at results that are artifacts of artificial programming
>side-effects, and are not results due to mathematics proper.
But these effect you label "artificial side-effects", are no different that what a human might achieve. That is if you don't see a way to re-arrange things or do things in a different order you likely to get the same results as Mathematica does.
Take the example you used when you started this thread. If you gave the results of the integral with the same denominator, m^2 - n^2, a human, they either have the same problem with division by zero when m = n or must take the appropriate limit. Taking the appropriate limit is an additional step. It is no different when using Mathematica.
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